Random matching problems on the complete graph
Journal article, 2008
The edges of the complete graph on n vertices are assigned independent exponentially dis-
tributed costs. A k-matching is a set of k edges of which no two have a vertex in common. We
obtain explicit bounds on the expected value of the minimum total cost Ck,n of a k-matching.
In particular we prove that if n = 2k then π2 /12 < ECk,n < π2 /12 + log n/n.